一类特殊矩阵的逆矩阵的特点及求逆公式

Characteristic and the Formula for Finding Inverse Matrices of a Simple Special Matrix

文章主要研究一类形如A=aij n×n其中aij=0,i+j>n+1aij≠0,i+j≤n+1的特殊矩阵,主要得出两个结果:其一,通过利用可逆矩阵的定义得到了上述矩阵其逆矩阵的一些特点;其二,利用幂零矩阵和严格上三角形矩阵的性质得到了求其逆矩阵的一个简单公式,这为解决矩阵方幂的计算问题提供了方便。

This paper mainly study a class of special matrices,such asA=aijn×n aij=0,i＋jn＋1aij≠0,i＋j≤n＋1 and abtain two results：first,by using definition of reversible matrix,we abtain some of the characteristics of its inverse matrix,which is mentioned in the front;Second,by using the property of nilpotent matrix and strictly up-triangular matrix,seeking its a simple formula for its inverse matrix,which helps to calculate a kind of up-t riangular matrix＇s power problem.